APMA 0350

Welcome to APMA 0350, an exciting dif-fun-rential equations adventure awaits you! On this website, you can find the syllabus, lecture notes, homework assignments, and study materials.

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Syllabus 

APMA 0350 – Syllabus (Summer 2024)

Homework Extension Request Form

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Lecture Notes

Note: The lecture notes will be frequently updated. Please refresh your webpage so that you have the most up-to-date version of the notes. 

#	Date	Lecture Notes	Lecture Videos
0	Jun 17	APMA 0350 Syllabus	Welcome to APMA 0350
1	Jun 17	What is a differential equation?	What is a differential equation?
			Basic ODE
			Solutions of ODE
			Existence and uniqueness
2	Jun 17	Direction Fields	Classification of ODE
			Direction fields
			dfield app
			Pretty pictures
3	Jun 18	Qualitative Methods	Autonomous ODE
			Logistic Equation
			More Qualitative Study
4	Jun 18	Existence and Uniqueness	Existence and Uniqueness
			ODE with a Twist
			Dangerous ODE
			Existence Uniqueness Theorem
5	Jun 20	Separation of Variables	Motivation
			Separation of Variables
			Implicit Solutions
			Why this works
			Logistic Equation
			Hidden Solutions
6	Jun 20	Integrating Factors	Motivation
			Integrating Factors: Simple
			Integrating Factors Example
			Integrating Factors: General
			Why this works
			Integrating Factors Practice
7	Jun 24	Applications	Falling Object
			To the Moon
			More to the Moon
			Compartmental Models
			Chemical Tanks
8	Jun 24	Exact Equations	Exact Equations
			Multivariable Review
			Solving Exact ODE
			Exact ODE Practice
			Nonexact equations
			Why this works
9	Jun 25	Euler’s Method (I)	Euler’s Method Motivation
			Euler’s Method
			Euler’s Method Practice
10	Jun 25	Euler’s Method (II)	Error
			Problems with Euler
			Variations of Euler
			Python Implementation
			dsolve app
11	Jun 26	Second-Order ODE	Second-Order ODE
			Factoring Method
			Distinct Roots Practice
			Repeated Roots
			Repeated Roots Practice
12	Jun 26	Complex Roots	Complex Numbers
			Complex Roots
			Complex Roots Practice
			Summary: 3 Cases
12.5	Jun 26	Exam 1 – Review	Integrating Factors
			Separation of Variables
			Exact Equations
			Second-Order ODE
			More Second-Order ODE
	Jun 27	Exam 1
	Jul 2	Exam 1
13	Jul 1	Boundary-Value Problems	Motivation
			Boundary-Value Problems
			Derivative Example
14	Jul 1	Undetermined Coefficients	Inhomogeneous Equations
			Undetermined Coeffs: Rule 1
			Undetermined Coeffs: Rule 2
			Undetermined Coeffs: Rule 3
			Sums of Terms
			Resonance
			Who’s that particular solution?
15	Jul 2	Mech and Forced Vibrations	Mass Spring Demo
			Mass Spring Derivation
			Free Vibrations
			Damping
			Forcing
			Resonance
16	Jul 2	Variation of Parameters	Cramer’s Rule
		The Wronskian (optional)	The Wronskian
			Variation of Parameters
			Var of Par Derivation
			Var of Par Practice
17	Jul 3	The Laplace Transform	Laplace Transform
			Laplace Transform Examples
			Tabular Integration
			Laplace Miracle
18	Jul 3	Applications to ODE	Applications to ODE
			Inhomogeneous Example
19	Jul 8	Step Functions (I)	Step Functions
			Simple Jumps
			General Jumps
			Jump Practice
			Reverse Way
20	Jul 8	Step Functions (II)	Shifting
			Reverse Way
			Summary: Four Cases
			Completing the Square
			Putting everything together
21	Jul 9	ODE with jumps	ODE with jumps
			ODE with shifts
22	Jul 9	Dirac Delta	Dirac and Roll
			Dirac Delta Construction
			Dirac Delta Laplace Transform
			ODE with Dirac Delta
			More Practice
23	Jul 10	Convolution	Convolution
			Convolution and ODE
			Integral Equations
			Integro-Differential Equation
			The Laplast One
24	Jul 10	Exam 2 – Review	Laplace Transforms
			Inverse Laplace Transforms
			Variation of Parameters
			Who’s that particular solution?
	Jul 11	Exam 2
	Jul 16	Exam 2
25	Jul 15	Systems of ODE (I)	Systems of ODE
			Matrix Form
			Higher-Order ODE
26	Jul 15	Linear Algebra Review	Eigenvalues and Eigenvectors
		Full Version	How to find eigenvalues
			How to find eigenvectors
			Diagonalization
27	Jul 16	Systems of ODE (II)	Solving Systems of ODE
			Why this works
			Phase Portraits
			Initial Conditions
28	Jul 16	Complex Eigenvalues	Complex Eigenvalues
			Complex Eigenvalues Practice
			pplane app
29	Jul 17	Repeated Eigenvalues	Repeated Eigenvalues
			Why this works
		Peyamstagram	Peyamstagram
30	Jul 17	Matrix Exponentials (I)	Matrix Powers
			Matrix Exponentials
			Proof of Facts
			ODE and Matrix Exponentials
			Matrix Exponential Practice
31	Jul 18	Matrix Exponentials (II)	Repeated Eigenvalues
			Repeated Eigenvalues Practice
32	Jul 18	Undetermined Coefficients	Undetermined Coefficients
			Undetermined Coeff Practice
			Who’s that particular solution?
			Resonance
33	Jul 22	Variation of Parameters	Variation of Parameters
			Why this works
			More Practice
34	Jul 22	Nonlinear Systems	Nonlinear Systems
			Equilibrium Points
			Classification
35	Jul 23	Ecology: Competing Species	Competing Species
			Equilibrium Points
			Classification
			Conclusion
36	Jul 23	Epidemiology: COVID Model	COVID Model
			Re-scaling time
			COVID outbreaks
37	Jul 24	Exam 3 – Review	Prologue
			Nonlinear ODE
			Chemical Tanks
			Variation of Parameters
			Who’s that particular solution?
			Epilogue
	Jul 25	Exam 3
	Jul 30	Exam 3

 

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Assignments

Homework	Due Date	Solutions
Homework 1	Jun 21	Solutions
Homework 2	Jun 29	Solutions
Non-Homework	Never due	Solutions
Mini Project	Jul 5
Homework 3	Jul 5	Solutions
Homework 4	Jul 12	Solutions
Non-Homework	Never due	Solutions
Programming	Jul 19
Homework 5	Jul 19
Homework 6	Jul 26
Non-Homework	Never due	Solutions

 

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Youtube Playlists

Chapter	Playlist
1	Introduction
2	First-Order ODE
3	Second-Order ODE
4	Laplace Transforms
5	Systems of ODE
6	Nonlinear ODE

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Exams

Exam 1: Thursday, June 27 until Tuesday, July 2 at 11:59 pm, covers Lectures 1-12

Practice Exam	Solutions	Comments
Study Guide
Mock Midterm 1	Solutions	Ignore 6
Mock Midterm 2	Solutions	Ignore 2, 3
Mock Midterm 3	Solutions	Spring 2023 Midterm 1
Mock Midterm 4	Solutions	Summer 2023 Midterm 1
Mock Midterm 5	Solutions	Fall 2023 Midterm 1
Mock Midterm 6	Solutions	Spring 2024 Midterm 1
Exam 1	Solutions	Summer 2024 Exam 1
Midterm 1 – Review
More Midterm 1 Review		Courtesy Caleb Evert
Introduction		Chapter 1 Playlist
First-Order ODE		Chapter 2 Playlist
Second-Order ODE		Chapter 3 Playlist

Exam 2: Thursday, July 11 until Tuesday, July 16 at 11:59 pm, covers Lectures 11-24

Practice Exam	Solutions	Comments
Study Guide
Laplace Table
Mock Midterm 1	Solutions	Ignore 5
Mock Midterm 2	Solutions	Ignore 5
Mock Midterm 3	Solutions	Spring 2023 Midterm 2
Mock Midterm 4	Solutions	Summer 2023 Midterm 2
Mock Midterm 5	Solutions	Fall 2023 Midterm 2
Mock Midterm 6	Solutions	Spring 2024 Midterm 2
Exam 2	Solutions	Summer 2024 Exam 2
Midterm 2 – Review
Second-Order ODE		Chapter 3 Playlist
Laplace Transforms		Chapter 4 Playlist

Exam 3: Thursday, July 25 until Tuesday, July 30 at 11:59 pm, covers Lectures 25-37

Practice Exam	Solutions	Comments
Study Guide
Mock Final 1	Solutions	Only do 6, 7
Mock Final 2	Solutions	Only do 6, 7
Mock Final 3	Solutions	Only do 6, 7
Mock Final 4	Solutions	Fall 2022 Midterm, do 3-5
Mock Final 5	Solutions	Fall 2022 Final, do 3-5, 8
Mock Final 6	Solutions	Spring 2023 Final, do 7-10
Mock Final 7	Solutions	Summer 2023 Final
Mock Final 8	Solutions	Fall 2023 Final, do 7-10
Mock Final 9	Solutions	Spring 2024 Final, do 7-10
Exam 3 – Review
Systems of ODE		Chapter 5 Playlist
Nonlinear ODE		Chapter 6 Playlist

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